A Nonlinear Dynamic Switched-Mode Model of Twin-Roll Steel Strip Casting

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Florian Browne ◽  
George T.-C. Chiu ◽  
Neera Jain
Keyword(s):  
Moving Boundary ◽  
Steel Strip ◽  
Phase Region ◽  
Strip Casting ◽  
Reduced Order Model ◽  
Mushy Region ◽  
Order Model ◽  
Roll Steel ◽  
Reduced Order ◽  
Twin Roll

During twin-roll steel strip casting, molten steel is poured onto the surface of two casting rolls where it solidifies to form a steel strip. The solidification process introduces a two-phase region of steel known as mushy steel which has a significant effect on the resulting quality of the manufactured steel strip. Therefore, an accurate model of the growth of mushy steel within the steel pool is imperative for ultimately improving strip quality. In this paper, we derive a reduced-order model of the twin-roll casting process that captures the dynamics of the mushy region of the steel pool and describes the effect that the casting roll speed and gap distance have on the solidification dynamics. We propose a switched-mode description that leverages a lumped parameter moving boundary approach, coupled with a thermal resistance network analogy, to model both the steel pool and roll dynamics. The integration of these models and simulation of the combined model are nontrivial and discussed in detail. The proposed reduced-order model accurately describes the dominant dynamics of the process while using approximately one-tenth of the number of states used in previously published models.

Dynamic Modeling of Twin-Roll Steel Strip Casting

2016 ◽  
Author(s):  
Florian Browne ◽  
George Chiu ◽  
Neera Jain
Keyword(s):  
Moving Boundary ◽  
Steel Strip ◽  
Solidification Process ◽  
Strip Casting ◽  
Roll Steel ◽  
Roll Casting ◽  
Solid Region ◽  
Explicit Consideration ◽  
Semi Solid ◽  
Twin Roll

We consider the problem of dynamic coupling between the rapid thermal solidification and mechanical compression of steel in twin-roll steel strip casting. In traditional steel casting, molten steel is first solidified into thick slabs and then compressed via a series of rollers to create thin sheets of steel. In twin-roll casting, these two processes are combined, thereby making control of the overall system significantly more challenging. Therefore, a simple and accurate model that characterizes these coupled dynamics is needed for model-based control of the system. We model the solidification process with explicit consideration for the mushy (semi-solid) region of steel by using a lumped parameter moving boundary approach. The moving boundaries are also used to estimate the size and composition of the region of steel that must be compressed to maintain a uniform strip thickness. A novelty of the proposed model is the use of a stiffening spring to characterize the stiffness of the resultant strip as a function of the relative amount of mushy and solid steel inside the compression region. In turn this model is used to determine the force required to carry out the compression. Simulation results demonstrate key features of the overall model.

A Nonlinear Reduced Order Model for Estimation and Control of Vacuum Arc Remelting of Metal Alloys

2005 ◽  
Author(s):  
Joseph J. Beaman ◽  
Rodney L. Williamson ◽  
David K. Melgaard ◽  
Jon Hamel
Keyword(s):  
Moving Boundary ◽  
Reduced Order Model ◽  
Vacuum Arc ◽  
State Variables ◽  
Order Model ◽  
Electrode Gap ◽  
Reduced Order ◽  
Vacuum Arc Remelting ◽  
Integral Methods ◽  
Estimation And Control

Vacuum arc remelting (VAR) is an industrial metallurgical process widely used throughout the specialty metals industry to cast large alloy ingots. The VAR process is carried out in a vacuum with the aim of melting a large consumable electrode (.4 m in diameter and 3000 kg in mass and larger) in such a way that that the resulting ingot has improved homogeneity. The VAR control problem consists of adjusting arc current to control electrode melt rate, which also depends on the electrode temperature distribution and adjusting electrode ram speed to control the arc gap between the electrode and the ingot. The process is governed by a 1 dimensional heat conduction partial differential equation with a moving boundary, which leads to an infinite dimensional, nonlinear system. In addition to the process nonlinearity, the inputs and all of the available measurements are corrupted with noise. In order to design a controller and a Kalman based estimator for this process, integral methods are used to derive a set of two coupled nonlinear ordinary differential equations in time, which capture the steady state and transient characteristics of melting in a VAR furnace. The model with the experimentally measured noise is then used to construct an estimator and a controller. The system can be described by two state variables that change in time: thermal boundary layer and melted length or alternatively electrode gap. The reduced order model compares favorably to an accurate finite difference model as well as melting data acquired for Ti-6Al-4V. It will be shown how this model can be used to obtain dynamic closed loop melt rate control while simultaneously controlling electrode gap. This controller and estimator were tested on a laboratory furnace at Timet.

Sign in / Sign up

Export Citation Format

Share Document